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According to British Army regulation, a column is a formation of soldiers in which each company of a battalion forms a line, and each line follows behind another line.
In column, each company is placed at a distance equal to its own breadth from the one immediately in front. A battalion in column thus occupies the same ground that it would cover in line, less the front of its leading company. A half column is formed with the companies at half distance. A quarter column is formed with the companies at 6 paces distance.
(I know that this is the 1870 manual and not the most recent version that would have been in use in the Boer Wars, but the text was unchanged and I can't find any later editions online).
In fact, there is a photo of a British Army battalion in South Africa in quarter column on page 58 of British Infantryman in South Africa 1877-81 by Ian Castle (Osprey 2003). As you can see, it is a close formation which would have left them vulnerable against an entrenched enemy, as at Magersfontein.